Sticky is a term used to refer to minions which are hard to remove from the battlefield, in general due to Deathrattles which summon other minions.
Strategy[]
Sticky minions can be very effective in countering AoE attacks such as 
Flamestrike and Lightning Storm. The summoning of further minions following the 'parent' minions' destruction prevents the play from clearing the board easily. In such cases the play can attempt to combine damage from multiple sources to provide a complete clear, or may simply have to accept that they are unable to clear the board entirely that turn.
Sticky minions are therefore an excellent counter to decks which rely on board-wide clears. Players using sticky minions may wish to keep these minions intact, even if this means losing overall attack potential, in order to deny the opponent the chance of an efficient board clear, especially given the relatively low Health of most of the resulting minions. However, under certain circumstances the player may intentionally choose to trade their sticky minions, such as when preparing for an attack using Bloodlust or Force of Nature, or intentionally trading a 
Haunted Creeper in order to activate a Knife Juggler. Sticky minions are also excellent targets for Deathrattle-synergies such as Reincarnate, Ancestral Spirit and Baron Rivendare.
Likewise, in many cases opponents will choose to ignore sticky minions rather than attempting to remove them through regular combat. This is especially true of Harvest Golem, whose offspring is as powerful as the Golem itself, and the Haunted Creeper, which actually increases in damage potential when destroyed. Opponents will often choose to ignore Haunted Creepers until an AoE removal option or other counter is available.
Eggs that summon minions (such as Nerubian Egg) are unusual in that almost their sole value lies in the triggering of their Deathrattle. Opponents are therefore almost guaranteed to ignore Eggs until they have a removal option available, while the controlling player is likely to want to either keep the Egg alive as a deterrent to AoE attacks, or give it Taunt in order to force the opponent to attack it. Players may also use Attack-granting effects like Abusive Sergeant to break open their own Egg.
Sticky minions are very useful for decks which are built upon buffing minions, or using auras or other effects that benefit from having multiple minions on the board. Sticky minions increase the likelihood that the player will have at least 1 minion on the board each turn, making cards like Defender of Argus easier to play to maximum effect.
Silences and Transform effects are a good counter to sticky minions. However, the low cost of most sticky minions often makes it impractical to employ this in every case. Mind control effects can be an excellent answer to sticky minions, and these also provide a particularly good target for Shadow Madness - the temporarily controlled target can be driven into combat with an enemy unit, with death of the sticky minion resulting in the 'child' minions being summoned permanently under the control of the stealing player.
Examples[]
