Let us first explain what a morpheme actually is. A morpheme is a representative unit of grammar that cannot be broken down into smaller meaningful parts. A morpheme is to language what an atom is to matter: its most basic and simple element.
When you break a word into syllables (granted, syllables are NOT morphemes), you must leave those chunks of words as they are because they cannot be broken any further. Those blocks that make up a word are its morphemes. An example is a word such as unkindness, where "un", "kind", and "ness" are the word's basic morphemes. None of these chunks can be broken down into smaller parts but they do serve a separate job within the word. This is why there are many different kinds of morphemes.
LEXICAL morphemes are only one type of morpheme. Also known as SEMANTIC morpheme (semantic=meaning), these morphemes are the basic units of the word that DO carry a meaning on its own. Using the same example, the lexical morpheme of the word unkindness would be the morpheme "KIND". Contrastingly, the morphemes un- and -ness are what is known as a GRAMMATICAL morphemes. For example, -ness is grammatical because the job that it does in the word is to transform it from an adjective "unkind", into a noun, "unkindNESS".