Mat 26:13 Verily I say to you, Wheresoever this gospel shall be preached in the whole world, [there] shall also this, that this woman has done, be told for a memorial of her.
Alternative: Truly I tell you that whenever they herald this good news in all of this society, they will talk also about her doing this in her rememberance.

Several aspects of this verse are interesting.

First, the verse is self-referential. It predicts a future in which this verse itself plays a part. Christ is predicting here not only that his message in general will be taught but that the specific experience that he is going through at the moment and his references to it will be taught. And indeed, this story is referenced in every Gospel (Mat 26:7, Mar 14:3, Luk 7:37, Jhn 11:2) as if the Gospel writers were obeying his command.

In each mention, the story is changed slightly. Matthew and Mark are the closest. In both, the location is Simon the Leper's house two days before the Last Supper. In Luke, it seems to happen much earlier in his ministry at the house of a Pharisee and the woman is described as a sinner. In John, the story is referenced first in the story about the rising of Lazarus and later as being at Bethany at a supper served by Martha and the woman is identified as Mary, Martha and Lazarus's sister. Writers disagree whether it was used on his head (Matthew, Mark) or feet (Luke, John). Mark and John both identify the ointment as spikenard. Mary and Martha are mentioned as sisters hosting Christ in another context where Martha criticized Mary for not helping and instead listening to Christ's teaching, and Christ defends Mary.

If the details differ, all agree that a woman annointed Jesus and washed his feet with her tears. This is the only example of someone doing a personal service for Jesus. The normal role is for Christ offering his services to others. Christ asks others for favors (water from the woman at the well, the loan of a horse or a room), but this is the only example of someone spontaneously doing a good deed for him.

This story is important, perhaps even critical, because it is Christ's only annointing in the Gospels. "Christ" (christos, christos) means "the annointed." Jesus is identified as Christ in Mat 1:1 and Peter describes him as "the Christ" (Mat 16:16) are Christ seems to accept that name in Mat 16:20, but publicly, Christ only uses that term "Christ" to refer the heir of King David (Mat 22:42) generally rather than to himself specifically.

Historically, the first annointing was of Aaron and his sons as the priests of Israel (Exd 28:41). This annointing of priests was passed down through the generations (Lev 16:32). Sacrifices, the altar (Exd 29:36) , and the tabernacle ( Exd 30:26) were also annointed. Samuel annointed Saul as the first King of Israel (1Sa 15:1) and later David (1Sa 16:13). David was anointed as king two more times, first by the elders of Judah (2Sa 2:4) and later by the elders of all Israel (2Sa 5:3). The other kings of Israel were also annointed at various times and places, but in rememberance of the annointing of David.

After his temptations, Christ's first words in the Gospel Mark are from Isaiah 61:1, which speak of being annointed to bring the good news. This story again unites the idea of an annointing with the spreading of the good news but now, right before his death.

"Good news" is from euangelion (euaggelion) a "reward of good tidings," a "thank offering for good tidings, " "good news," and "good tidings." Originally, this terms described a reward, like a tip, given to a messenger who brought good news.

"Preached" is from kêrussô (kerusso), which means means "to be a herald," "to officiate as an herald," "to be an auctioneer," "to make a proclaimation as a herald," "to proclaim," "to announce," "to preach," and "to teach publically."

"Told" is from laleô (laleo), which means "to talk," "to prattle," "to chat," "to talk," and "to speak." It also means "chatter" as the opposite of articulate speech.

"Whole" is from holos (holos), which means "the whole," "entire," "the universe," and "safe and shound."

"World" is from kosmos, which mean "order," "good order," "ruler," "world order," "universe," and "the world of men." Matthew uses it when Christ is talking about the order in the universe, specifically the order of the world of men, as it is designed to be.

"Memorial" is from mnêmosunon (mnemosunon), which means "remembrance," "memorial," and "reminder."