ITM options move more like the stock (higher delta) and cost more because they carry intrinsic-value. Deep ITM options have very little extrinsic-value and behave almost like a leveraged stock position.
ITM options at expiration are automatically exercised by most brokers, which can leave you with a stock position you did not intend. See assignment.
Example: stock at $88. The $80 call and the $95 put are both in the money; the $80 call by $8 and the $95 put by $7.
Related: out-of-the-money, at-the-money, intrinsic-value, delta