The short answer consists of two factors: (1) Economic disparity between East and West, and (2) decreasing birth rates.

(1) After the reunification in 1990, the economy of the GDR all but collapsed. East German industry and infrastructure was outdated and inefficient and couldn't really compete with that in the West. As the reunification meant completely unrestricted domestic freedom of movement, many East Germans went to the West in search of higher-paying jobs. The resulting shift in the labor supply closed the wage gap a little bit in the following years (more workers in the West=lower wages/less workers in the East=higher wages), but to this day unemployment rates in East Germany are higher and wage levels lower than in the West.

(2) Birth rates also decreased dramatically with the reunification. Socialist East Germany, despite the lower standard of living, had a significantly more pro-family government than the West: Managing family and job was easier and more strongly encouraged (state-run child care, youth programs, etc). With the reunification, these opportunities disappeared, people worked longer hours and having children became more inconvenient, leading birth rates to collapse.

These seem to be the two primary factors in the dramatic population decline in East Germany in the 1990s, naturally there were other factors, such as an aging population (which is naturally linked to the birth rate issue). Also note that most of this excludes Berlin, which as a major city is a special case and saw a continuous population increase.

My main sources for all this are this book and this website, although both are in German, so perhaps not of much help to you.

Also, this is my first time replying on this sub, so if a passing mod finds that my work is not up to the standard please let me know so I can improve :)

There was a lot of emigration to the western states, mostly for economical reasons. The unemployment rate in the states of the former GDR compared to the western states has been higher since the reunification (http://www.bpb.de/system/files/pdf/KUAAB0.pdf). And for those who had work, the average income was also lower (http://www.bpb.de/geschichte/deutsche-einheit/lange-wege-der-deutschen-einheit/47436/einkommen-und-vermoegen). This lead to emigration especially of younger people, hence also lowering the number of births.

Further reading (in german): http://www.bpb.de/geschichte/deutsche-einheit/lange-wege-der-deutschen-einheit/47253/zug-nach-westen, http://www.beauftragte-neue-laender.de/BNL/Navigation/DE/Themen/Gleichwertige_Lebensverhaeltnisse_schaffen/Demografie/Demografische_Situation/demografische_situation.html, http://www.berlin-institut.org/online-handbuchdemografie/bevoelkerungsdynamik/regionale-dynamik/ostdeutschland.html