What is accrual accounting or accrual accounting system?

According to accrual concept the income and Expense should only be recognized when they are incurred........not when they are actually paid

Accrual basis is one of the Generally Accepted Accounting Principles "GAAP".
It means that the transactions recognized and recorded in the books when it occurs regardless the receive or payment of cash.
So sometimes we see "Unearned Revenues" or "Prepaid Expenses", because we received or paid cash, respectively, but the revenue is not earned yet.

Accrual accounting system is the system where revenues and expenses are recognized when earned not necessarily when cash is received or paid.
So, for example, when a company provides a service, it records fees earned even if the payment for the service has not yet been received.
This is done by debiting Accounts Receivable and crediting Fees Earned.
This entry increases the revenue for the period.
Likewise, when an expense is incurred (such as telephone expense) it is recorded in the company books even though the cash may not have been paid out yet.
This entry decreases net income for the period.
With the accrual system, income and expenses are recorded in the period they are incurred and not in the period that cash is paid or received.
On the other hand, in the cash system, income and expenses are not recorded until cash has been received or paid.

There are two type of recording Cash and Accrual In Cash, we record expense when we paid and sale when we receive.
In Accrual, all expenses are recorded when incured either the payment is made or not, and record sale either cash receive or not.
By Accrual we are able to record all expenses and sale, By accrual a company can better understand about cost, income and expense and easily be understand too about the accurate profibility.

An accounting system wherein transactions are recorded in the books of accounts when these transactions take place and they are not recorded when cash is paid or cash is received

Accrual accounting is considered to be the standard accounting practice for most companies, with the exception of very small operations.
This method provides a more accurate picture of the company's current condition, but its relative complexity makes it more expensive to implement.
This is the opposite of cash accounting, which recognizes transactions only when there is an exchange of cash.
The need for this method arose out of the increasing complexity of business transactions and a desire for more accurate financial information.
Selling on credit and projects that provide revenue streams over a long period of time affect the company's financial condition at the point of the transaction.
Therefore, it makes sense that such events should also be reflected on the financial statements during the same reporting period that these transactions occur.
For example, when a company sells a TV to a customer who uses a credit card, cash and accrual methods will view the event differently.
The revenue generated by the sale of the TV will only be recognized by the cash method when the money is received by the company.
If the TV is purchased on credit, this revenue might not be recognized until next month or next year.
Accrual accounting, however, says that the cash method isn't accurate because it is likely, if not certain, that the company will receive the cash at some point in the future because the sale has been made.
Therefore, the accrual accounting method instead recognizes the TV sale at the point at which the customer takes ownership of the TV.
Even though cash isn't yet in the bank, the sale is booked to an account known in accounting lingo as "accounts receivable," increasing the seller's revenue.

"Accrual basis accounting" is an accounting system where income is reported when earned and expenses are reported when incurred, regardless of when the cash flows actually occur.

The accrual concept is an accounting system which recognizes revenue and expenses as they are earned or incurred respectively, without regard to the date of receipt or payment.

An accounting method that measures the performance and position of a company by recognizing economic events regardless of when cash transactions occur.
The general idea is that economic events are recognized by matching revenues to expenses (the matching principle) at the time in which the transaction occurs rather than when payment is made (or received).
This method allows the current cash inflows/outflows to be combined with future expected cash inflows/outflows to give a more accurate picture of a company's current financial condition.

The accounting method under which revenues are recognized on the income statement when they are earned (rather than when the cash is received).
The balance sheet is also affected at the time of the revenues by either an increase in Cash (if the service or sale was for cash), an increase in Accounts Receivable (if the service was performed on credit), or a decrease in Unearned Revenues (if the service was performed after the customer had paid in advance for the service).
It holds specific meanings in accounting, where it can refer to accounts on a balance sheet that represent liabilities and non-cash-based assets used in accrual-based accounting.
These types of accounts include, among others, accounts payable, accounts receivable, goodwill, deferred tax liability and future interest expense.

An accounting method that measures the performance and position of a company by recognizing economic events regardless of when cash transactions occur.
The general idea is that economic events are recognized by matching revenues to expenses (the matching principle) at the time in which the transaction occurs rather than when payment is made (or received).
This method allows the current cash inflows/outflows to be combined with future expected cash inflows/outflows to give a more accurate picture of a company's current financial condition.