In simple terms, meter refers to the rhythmic and syllabic structure of a piece of poetry, which is essentially what a hymn is. Meter markings on hymn tunes indicate the number of syllables in each line of the hymn. For instance:
A hymn with the meter 76 76 has seven syllables in the first line, six in the second, seven in the third, and six in the fourth. A hymn with the meter of 10 10 10 10 has four lines, each with ten syllables. The letter D at the end of a meter notation means "double." For instance, a hymn with the meter 87 87 D has eight syllables in the first line, seven in the second, eight in the third, seven in the fourth, then the pattern repeats itself for the fifth through eighth lines.
Some meters are used so frequently they have acquired names of their own:
86 86 is known as Common Meter (abbreviated CM)
66 86 is known as Short Meter (abbreviated SM)
88 88 is known as Long Meter (abbreviated LM)
Again, when the letter D follows any of these, the pattern is repeated.
When looking at the metrical index of a hymnal, one often finds some hymns listed with the meter "Irregular." This means a couple of different things. For one, it can mean there is no consistent pattern of number of syllables per line. For another, it can mean the number of syllables per line is not consistent between stanzas. This can happen especially when slurs are used in some stanzas and not in others in the same part of the music.
In addition, most hymnals do not count out the number of syllables in refrains. Thus, if a hymn is listed as "CMD with Refrain," it means the stanzas are Common Meter Double, and the refrain is in addition. The only way to know for sure is to count the syllables in the refrain.