Learn Spanish (Latin America): Se corta el tallo para plantar el esqueje.

This uses the passive se. While el tallo es cortado is grammatically correct, Spanish strongly prefers using se + a third-person verb to express that something is done when the person doing the action isn't specified. The literal passive voice often sounds unnatural or translated from English.

This lesson is about conditional gerunds. Could I use one here to express the same idea?

Not without changing the meaning slightly. Here, para plantar expresses purpose (in order to plant). A conditional gerund expresses a condition (if/by doing X). You could rephrase the idea as Cortando el tallo, puedes plantar el esqueje (By cutting the stem, you can plant the cutting), which turns it into a condition rather than a statement of purpose.

Why do we use the infinitive plantar instead of a conjugated verb?

Because the implicit subject of the first action (whoever cuts the stem) is the same as the implicit subject of the second action (whoever plants the cutting). When the subject doesn't change, Spanish uses para + infinitive. You would only use para que + subjunctive if a specific, different person were doing the planting.

What exactly is an esqueje?

An esqueje is a cutting or slip in gardening. It refers to a piece of a plant, usually a stem or leaf, that is cut off and placed in soil or water to grow a completely new, cloned plant. It is an essential vocabulary word for anyone talking about houseplants or agriculture in Spanish.