The use of the 2♦ and 2♥ (and often 2♠) responses to an opening 1NT bid as transfers is one of the most widely employed conventions in the game.
The initial purpose of the convention was to make the notrump opener the declarer in a suit contract when his partner held a relatively weak hand with a long suit; this would make the opening lead come up to the stronger hand and such a situation is advantageous should declarer possess one or more tenaces or tenuously guarded honors.
The use of "bouncing" and "breaking" rebids by opener offered partnerships the opportunity to find safe game and slam contracts with fewer high card points than with traditional methods.
Since a 1NT opening bid requires a balanced hand, i.e. no more than one doubleton, it promises to have at least two cards in the desired suit: Opener can super-accept the transfer by bidding three of the major with a maximum hand containing at least four cards in that major.
As promulgated by Paul Mendelson, they are: With these two devices (bouncing and breaking) it is possible to discover, at very little risk, games that would otherwise be missed.