An applicative marker is a grammatical marker occurring on a verb that changes the verb's valency in such a way that an argument other than the P of the base verb gets to be coded like the P-argument in a simple transitive clause.
There are various subtypes of applicative markers, depending on the role which they transform into a P-argument. Thus, for example, an instrumental applicative marker is an applicative marker that transforms a nominal with an instrumental role into a P-argument, and languages often have benefactive or comitative applicative markers.
–– Polinsky (2005), Peterson (2007) and Pacchiarotti (2017) offer general cross-linguistically informed discussions of applicatives, and Pacchiarotti's Chapter 2 has extensive discussion of the terminology.
–– Many authors think of applicative constructions as containing an additional "direct object" of some kind, and then the question of the cross-linguistic identification of "direct object" arises. The definition in terms of "P-argument" (= coded like the monotransitive P) solves this problem.
–– Some languages have object-adding markers that indicate the addition (or mere presence) of a different kind of "object", e.g. a dative or oblique object, or even an adpossessor of an object. Such constructions are not applicatives by the definition given here, though they are of course very similar to them and may be treated identically in particular languages.