Just to point out, Klement Gotwald, Who was responsible for the Putsch in Czechoslovakia in 1948, and consequently became the leader of the country was also embalmed and put on display at the National Monument in Vitkov. Stalin was also embalmed and put on display next to Lenin. Both men were removed and buried (cremated in Gottwald's case) due to De-Stalinization and unsuccesful embalming techniques.

Embalming and public display were important aspects of the cult of personality these Leaders carefully cultivated around themselves; in essence to make themselves corporeally immortal. Their mausolea were also generally built in nationally significant areas (such as Vitkov for Gottwald which was and continues to be a monument to Jan Zizka and the Czechoslovak Legionnnaires)

Georgi Dimitrov, the first communist leader of Bulgaria and Khorloogiin Choibalsan, the leader of the Mongolian people's republic were likewise embalmed and put on display in mausolea. They were later removed (1989 and 2006) and buried with the mausolea torn down (in 1999 and 2006).

A good example of currently embalmed and on display leaders that cultivated extensive cult of personalities are Kim Il-Sung and Kim Jong-Il of North Korea. Often, the modern embalming of other authoritarian leaders (like Gottwald and the Kims) was directly reliant on the experience and know-how derived from the embalming of Lenin.

After Lenin's death his body was considered by the top politicians to be an important propaganda symbol. There were two options considered at that time: freezing, supported by Leonid Krasin, and embalming eventually performed by anatom Vladimir Vorobiev and chemists Boris Zbarsky. It should be mentioned that Lenin's relatives were against any preservations. Krasin was a Foreign trade minister in the Bolshevik government and a follower of a contemporary Russian philosopher Nikolai Fyodorov who argued that mortality will eventually be eliminated and not only living people will be immortalized but also dead people will be resurrected by scientific methods. So for Krasin it was not just a propaganda move but an attempt to immortalize Lenin. The problem with freezing was that it didn't work well, but there was also no efficient embalming techniques as it was not common. So Vorobiev and Zbarsky performed a set of experiments and in about 4-5 months solved the problem rather successfully. My guess that after that embalming of Mao Stalin etc. was just copycatting.

Sources:

Lopouhin Yu.M. Disease, death and embalming of V.I. Lenin: Truth and myths. (in Russian).

Wikipedia pages for Krasin, Zbarsky (Russian), Vorobiev (Russian), Fyodorov.

Edit: spelling.

The preservation of the corpse of the founder/leader/head of state is absolutely an outgrowth of communism's whole psychological nature in general.

The State is a body. This is a common analogy in most political systems, and may be an ancient anthropological commonality.

Communism, however, has a particular philosophy of immanence that denies any transcendence. Therefore, the body of the founder must be preserved. Like the State itself under communism, the body is kept together and saved from decomposition by sheer force of will and technocratic intervention. Totally artificial, but an act of power (back when this started, it wasn't as easy as getting someone plastinated; keeping a body in such a condition was a "miracle" that only the State had the resources to achieve).

Basically, start thinking of the communist state as "a non-organic body" and you'll understand why it would make sense to preserve the State Body (symbolized by the body of the founder) by artificial intervention. The attitude of communists towards the bodies of their state founders...is exactly analogous to the attitude they take with regards to the Body Politic.

The idea is that by its technocratic might, the Body saves itself from decomposition. Communism believes itself to have "beaten death" and mortality, in this sense, in a totally immanent, non-transcendent way. The only caveat is that the preservation/immortality they've achieved isn't organic life either, but a static corpse held together by sheer will and state power.