At last a pair of botanical words!
Xylem and Phloem are the two types of tissue in plants which transport food and water around the plant.
Xylem [z-eye-lem]
The supporting and water-conducting tissue of vascular plants; woody tissue.
This is the network of tubes through which the plants move water from bottom to top. It also forms a large part of the woody (supportive) structure of the plant. It is concentrated in the centre of the stem.
As might be expected the derivation is from the Greek ξύλον, wood.

Phloem [flo-em]
The food-conducting tissue of vascular plants.
The network which transports food (mostly sugars) from the leaves where they are produced by photosynthesis to the growing tissue.
The phloem is softer tissue that the xylem and occurs mostly in the layer just under the bark where the latest “tree ring” is growing.
Again derived from the Greek: ϕλόος = ϕλοιός, bark + -ηµα (passive suffix).
All (vascular) plants, ie. the vast majority we meet in daily life, conform to this basic model even if they appear to be soft rather than woody. However as you would expect the reality is a lot more complex than the above explanation!