Mat 16:24 If any [man] will come after me, let him deny himself, and take up his cross, and follow me.

The topic of the chapter is the connection between the spiritual and physical, where the spirit is the seed creates physical existence or the motivation that inspires a physical action. Here, Christ is saying that to follow him, we must foget about our concerns with self and take up our burdens and emulate him. In other words, we shouldn't be afraid of the threats that face us but inspired by them to copy his example.

"Come" is from erchomai, which means "to come" and "to go." It means "to set out" and "to arrive at." It is a little like we use the phrase "he is on his way," which can mean either that he is coming or going.

"Deny" is from aparneomai, which is the future form of aparnos "to deny utterly," and "to reject." It is from the noun aparnêsis which means a "denial" and a "rejection."

"Take up" is from aeirô, which means "to lift up," "to raise up," "to take up," ""to exalt," and "to remove." It is used by Matthew in all these different senses in his gospel. In its passive form, it also means "to suspend" or "to hang," which seems relevant considering we are talking about crucifiction, however, Matthew never uses it in that way.

"Cross" is from stauros, which means "upright post or stake," and "a stake for impaling." In Matthew's time, it was used for describing specifically the stake used for crucifiction.

"Follow" is from akoloutheô, which means "to follow" or "to go after" someone. It is also a metaphor for being guided by someone. It also means "being consistent with" someone or something that has gone before.