Lincoln Memorial cents feature the word AMERICA on the reverse. The Close or Wide AM refers to the distance between the A and the M in AMERICA on struck coins. When the A and the M are a normal distance apart as compared to the other letters in AMERICA this is known as a Wide AM. When the A and the M are almost touching this is known as a Close AM.

 
Wide AM
Close AM

The interest in this is that there are rare instances where, in a particular year, the spacing on a small number of coins is different from the spacing on the vast majority of regular coins struck in that year.

Another characteristic that is used to differentiate these rare coins from others of the same year is the distance of the reverse designers initials, FG, from the right side of the memorial. On Close AM cents the initials are farther away from the memorial than on the Wide AM cents. Also, there is a horizontal serif on the end of the straight vertical part of the G on the Wide AM cents.

 
Wide AM
Close AM

In 1993 the reverse side design of both business strikes and proof coins transitioned from the Wide AM as normally found on 1992 and prior cents to a Close AM design. However a few 1992 cents were produced with the newer Close AM design of 1993 instead. These are rare and valuable.

For proof coins in 1994 the mint reverted back to the Wide AM design so that proofs and business strike coins up to 2008 have the opposite design on the reverse sides. In 2009 the Shield cent replaced the Memorial cent with a new reverse entirely.

However in 1998, 1999, and 2000 some business strike coins were found having the wide AM design (using a proof reverse die) when the norm was then the Close AM design. These are also valuable but not as rare as the 1992 cents. Also in 1998 and 1999 some proof coins were struck with the Close AM design (using a business strike die) making them also valuable.

To summarize the following is normal:

What this means is that the following list of confirmed variations from these rules are valuable in order from most to least rare:

On more thing, in 1988 rare alternate reverses from both the Philadelphia and Denver mints were produced where the A and the M were Wide as normal but the FG initials were close to the memorial rather than far as they should be for that year. These are 1988 coins with the transitional year reverse of 1989. This variety has sometimes been unfortunately called the 1988 Wide AM even though a Wide AM is normal for that year.

 

If all this is too confusing then perhaps a better explanation can be found by understanding that there were eight different Reverse Die Varieties (RDV) used on the Memorial Cents from 1959 to 2008. These are well listed at Variety Vista. The collectible coins are those that deviate from the norm in the year the coin was minted. The 1988 cents of interest normally struck with RDV-005 instead were produced with a 1989 RDV-006 die. The 1992 cents of interest normally struck with RDV-006 instead were produced using a 1993 RDV-007 die.

The other coins of interest listed above were either business strike coins struck with a proof die or a proof coin struck with a business strike die.