Measure words are used in noun phrases between the demonstrative and/or number and the main noun.
The order is 这/那 + Number + Measure word + Noun.
For example:
三张名片 (sān zhāng míngpiàn) three MEASURE WORD name cards.
这张名片 (zhè zhāng míngpiàn) this MEASURE WORD name card.
There are two types of measure words, some represent an actual measure, e.g. 'two cups of tea', 'a sheet of paper', others function as classifiers, that is, they indicate what kind of object the noun represents.
The most common classifier is 个 (ge) it is used with most abstract nouns. Most concrete nouns have specific classifiers that in some way reflects the physical appearance of the noun. For example the classifier 张 is used for objects with a flat surface like paper, tables or beds.
Classifiers are best learned together with the noun:
一个人 yī gè rén a person
一张名片 yī zhāng míngpiàn a name card
三口人 sān kǒu rén three people
Most measure words do not have an English equivalent unless they refer to an actual quantitative measure, as in the English 'A cup of coffee ' 一杯咖啡 (yī bēi kafēi).