There are two kinds of measure words, quantifiers and classifiers. Quantifiers indicate the amount or number of things denotated by the associated noun. They often have equivalents in English. Classifiers indicate the kind of thing the noun refers to. There are a large number of classifiers in Chinese, especially with concrete nouns. Abstract nouns tend to use the generic 个 (gè) as a classifier. After 这 (zhè) 'this', 那 (nà) 'that' and any numerals quantifiying the noun a measure word is obligatory.
Examples:
一壶绿茶 (yī hú lǜ chá) 'a pot of green tea' Numeral - measure word (quantifier) noun
一盘点心 (yī pán diǎnxīn) 'a plate of snacks' Numeral - measure word (quantifier) noun
一瓶红酒 (yī píng hóng jiǔ) 'a bottle of red wine' Numeral - measure word (quantifier) noun
一杯咖啡 (yī bēi kāfēi) 'a cup of coffee' Numeral - measure word (quantifier) noun
Classifiers are often not translated into English:
那两本书 (nà liǎng běn shū) 'those two books'
这个人 (zhè ge rén) 'this person'