From BR Bullpen

A draft-and-follow is a player selected usually in the later rounds of the amateur draft by a team that does not intend to offer him a contract immediately . The typical draft-and-follow pick will be attending a junior college or will be a college player with at least a year of eligibility remaining as a player. The team that drafts him has a year to decide whether to offer him a professional contract before the player becomes eligible for the next year's amateur draft. This allows the drafting team to see him play for another season before making this decision.

If a player blossoms during his additional year of play, the drafting team can end up with the rights to a player who would normally have warranted a much higher draft pick. The team is expected, however, to reflect this in its contract offer. If not, the player who knows that his value has risen significantly can 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 have to agree to contract terms with drafted players by August 15, meaning that teams have barely two months to make a decision about signing a particular player. Any player unsigned at that date automatically returns 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.