Nolimar (also known as Solomar) refers to the practice of using Olimar (or Alph) without any Pikmin, either due to losing Pikmin from them being KO'd and being forced into the situation, or by choosing to play the entire match with no Pikmin.
Without Pikmin, Olimar only has six attacks: his jab's two hits, his three tilts, his dash attack, and his neutral aerial. Nolimar is capable of racking up damage with most of these moves, with his forward tilt and dash attack being his KO moves. Combined with the hop from a blank Pikmin Chain in Brawl, and the Super Armour of Pikmin Order, it is possible to win a match as Nolimar despite his pitiful KO power and major problems with stale moves; of course this is incredibly difficult.
Note that at the start of a match, Olimar will automatically pluck three Pikmin during his entrance, so to intentionally play as Nolimar, the player will have to use Pikmin Throw or his forward smash to throw the Pikmin off of the stage, have the Pikmin attacked, have Olimar KO'd, or simply choose to never use Pikmin-based attacks - though the Pikmin can still interfere with opponents by being hit in this case.
In SSB4, Olimar's abilities without any Pikmin were slightly buffed, most notably by the removal of Pikmin Chain in favour of Winged Pikmin (which, despite not being treated as Pikmin by the game, could be argued to violate the spirit of Nolimar due to technically being Pikmin), and the improved reach on his jab, and higher knockback on his forward tilt, though it's worth noting that Pikmin Order has fewer armour frames than in Brawl.
Nolimar is a popular character to use in gag matches/taunt matches.