The Torah commands us to take a "peri eis hadar," known to us as an "etrog." At times, a farmer will combine a lemon and etrog tree; this is called grafting. The poskim discuss the identity of the fruit of this tree, and whether a "grafted" etrog is still considered to be an etrog.
The Rema (Teshuvot HaRema 117) rules that one should not use an etrog murkav (grafted etrog). This opinion appears to have been the consensus of the Rabbis of Sfat in the 16th century, including R. Moshe ben Yosef di Trani, known as the Mabit.
The Rishonim attempt to provide characteristics which might identify a grafted etrog. For example, some wrote that if the etrog is very smooth, or the oketz sticks out, it may be a grafted fruit. Others noted that while if one cuts open a lemon, he will find a lot of pulp, an etrog has very little pulp, as a thick peel surrounds it. Furthermore, the seeds of an etrog are aligned vertically, while the seeds of a lemon (or a grafted etrog) might be horizontal. The Hatam Sofer notes that these characteristics may not be accurate.
Therefore, one must be careful to buy an etrog from an orchard with a tradition. For example, the Hazon Ish only used etrogim from the orchard of Rav Michel Yehudah Lefkowitz; to this day some use only etrogim produced by trees planted from seeds of this original tree. R. Ovadia Yosef and Hacham Ben Sion used "Yemenite etrogim." When the Jews came to Israel from Yemen, they brought with them etrog seeds, which they insist have a tradition of being from pure etrogim.
It is worth noting the opinion of R. Alfanderi (Teshuvot OH 13), who wrote that a grafted etrog is valid. R. Ovadia Yosef maintained that one should not rely upon this opinion.
Summary: One should be careful to purchase etrogim from an orchard which maintains a tradition that their etrogim are not grafted, as almost all halachic authorities invalidate grafted etrogim.
