What is "lechatchilah", "mehudar" & "bedieved"?
In all areas of halachah, Jewish law, there are varying opinions as to how to fulfill each mitzvah, law or commandment. Some opinions are contradictory, meaning one can fulfill one or the other but not both while other opinions are complementary, meaning one can theoretically fulfill both or several opinions. In each generation Halachic authorities and codifiers have determined which opinions to follow. ("Do A not B" or "It is sufficient to fulfill the mitzvah by doing A") Satisfying the law as determined by our leading halachic authorities is called fulfilling the halachah lechatchilah, at the preferred halachic level or standard. If one fulfills the halachah lechatchilah and in addition fulfills another or several complementary opinions he will have surpassed the (Minimal) preferred halachic standard - fulfilling the law with hiddur. The more opinions he fulfills the more mehudar is his fulfillment of the mitzvah and/or the more mehudar is the object of the mitzvah. Mehudar is translated as enhanced.
One who is unable to fulfill the mitzvah lechatchilah but nevertheless fulfills the law according to opinions that the halachic authorities didn't decided according to is considered to have fulfilled the mitzvah, in most cases, bedieved. His non preferable fulfillment of the halachah may be due to financial constraints or lack of knowledge. Additionally, he may have been fulfilling the mitzvah lechatchilah but due to changes in the physical circumstances of the object of the mitzvah, i.e. tefillin, he may, knowingly or unknowingly, be fulfilling the mitzvah bedieved. Therefore, circumstances, i.e. financial, may allow such an individual to fulfill the mitzvah bedieved and for him it may even be considered as if his fulfillment is lechatchilah. In cases where one does not realize he is fulfilling the mitzvah bedieved or learns of this after the fact/purchase, even though he should not fulfill the mitzvah in such a manner, he would still be considered as fulfilling the mitzvah ex post facto.
Mehudar, Another Side to It
Mehudar also means aesthetically enhanced. The Torah states, "This is my G-d and I will glorify him". From here we learn that it is proper to adorn the mitzvahs by making the actual objects used in their fulfillment appear beautiful or to form them from precious materials or to house them in attractive or precious holders. Just as we prepare a special meal or dress in our finest in expectation of an esteemed guest or for one we care deeply about so too by adorning the mitzvahs we express our deep commitment and love for G-d and his commandments. This does not obligate us to spend beyond our means yet we should make an effort to express how precious each mitzvah is, each according to his capabilities.