Grinding refers to creating an artificial need for currency (or experience) that involves gameplay that is not challenging but highly repetitive and absolutely necessary to unlock game content. Grinding encourages addictive type behavior, which is the cornerstone of the new Free2Play gaming movement since it allows game developers to create in-app purchases as an alternative and a way to allow players to experience faster novelty in a self-feeding loop.
Examples of games that feature grinding in a Free2Play setting in a way that encourages bad habits and addictiveness: Star Trek Online, Injustice Mobile, most popular puzzle games for mobile.
Examples of games that offer Free2Play with a revenue model that does not encourage addictiveness: DCUO
How are they different?
In the first set of examples, in-app purchases buy specific items which can then be used to play games of random chance that have a small chance of returning the desired item (ie lockboxes, booster packs for special cards).
In the second example, real money is used to pay for a time where these restrictions are removed and can be used as many times as desired, although other methods are used to throttle back the gameplay (ie making certain content available once a day/week). Players still have to build their levels which are the core of the gameplay in the same manner.
In simpler terms, "Sell a man a virtual fish, he'll play for a day, sell a man a license to use a virtual fishing pond for a week and he'll fish every day for a week."