'Leísmo' (in phonology) refers to the convention in some very minor dialects of Spanish (mainly Philippine) to pronounce the digraph 'll' as a lateral approximant or /l/, which is basically the 'l' sound in English. This is as opposed to the /j/ sound which it represents in most dialects (like the 'y' in 'yet', or the palatal lateral /λ/ that it represents in Castillian Spanish. This leísmo occurs when the phonology of languages native to the region do not allow for /λ/. Since the Spaniards who arrived in the Phillipines in the 1520s were lleísto and not yeísto, they brought the /λ/ vs. /j/ distinction with them, and since the Filipinos were not accustomed to the /λ/, it simply became /l/. This same thing happened in a few other places, but mainly the Philippines.
A person or dialect with leísmo is described as leísta (as opposed to yeísta or lleísto/a). Due to the leísmo, a distinction is made between valla/vaya, callo/cayo and llanto/yanto, but there is no distinction between cale/calle llora/lora or ele/elle. This can, of course be very handy in avoiding confusion on one end, but cause more in other areas of speech.
In morpho-syntax, leísmo refers to the use of 'le' instead of 'lo' for the direct object in some dialects. The 'le' is still used as the indirect object as well. In this way, 'Dámele' means 'give it to me' and 'le comí' means 'I ate it'. The opposite of this is 'loísmo, which also has a dual meaning.