Learn Spanish (Spain): La reunión empieza a las ocho y media.

The lesson teaches son las to tell the current time (like son las ocho for 'it is eight o'clock'). However, when you want to say at what time an event happens, you use a la or a las. Since eight is plural, we use a las ocho to mean 'at eight o'clock'.

Why is the word for half feminine (media)?

When telling time, media stands for media hora (half an hour). Because the word hora (hour) is a feminine noun in Spanish, you must use the feminine form media rather than the masculine medio.

Why is las plural if eight o'clock is just one specific time?

In Spanish, the hours are treated as a countable number of hours. Every hour from two to twelve is considered plural, so we use las. Only one o'clock is singular, meaning you would use la (for example, a la una).

Why is the verb empieza spelled with an ie?

The dictionary form of the verb 'to start' is empezar. This is what we call a stem-changing verb, meaning the middle e changes to ie in certain forms. Because la reunión (the meeting) acts as a third-person singular subject ('it'), the verb changes to empieza.