From BR Bullpen

A draft-and-follow was a player selected usually in the later rounds of the amateur draft by a team that did not intend to offer him a contract immediately. The typical draft-and-follow pick was attending a junior college or was a college player with at least a year of eligibility remaining. The team that drafted him had a year to decide whether to offer him a professional contract before the player became eligible for the next year's amateur draft. This allowed the drafting team to see him play for another season before making this decision.

If a player blossomed during his additional year of play, the drafting team could end up with the rights to a player who would normally have warranted a much higher draft pick. The team was expected, however, to reflect this in its contract offer. If not, the player who knew that his value had risen significantly could decide to refuse the contract offer and try his luck again in the draft.

In 2007, changes were made to the amateur draft which effectively eliminated the draft-and-follow. As of that year's draft, teams had to agree to contract terms with drafted players by August 15th, meaning that teams had barely two months to make a decision about signing a particular player. Any player unsigned at that date automatically returned to the draft pool for the following year. This change was done to prevent situations in which certain draftees did not know whether they would be going to school or playing professional baseball until literally the day on which classes were to start, something which was deemed to be neither in the interest of the schools nor of the player/students. It was also thought that by limiting the time during which negotiations were conducted, there would be pressure for players to sign for lower bonuses, allowing for a more even playing field among teams.