A brass instrument part doesn't have to be in constant motion to need lubrication. Case in point: the tuning slide. This only moves when you're adjusting or disassembling your instrument, but the last thing you'd want is for it to be seized-up when that time comes. And since the tuning slide is used for tuning (hence the name), it's important to be able to position it precisely. Doing so requires a smooth motion that glides easily into place, which is exactly what an application of tuning slide grease will get you. Plus, like any lubricant for brass instruments, tuning slide grease doubles as a protective coating, keeping the contact surfaces of your tuning slide in good condition over the lifespan of the instrument.
There are two main types of tuning slide grease: oils and creams. You can spot oils by looking for products that come in bottles, like Bach Tuning Slide Grease and Hetman Tuning Slide Oil. Creams, on the other hand, are packaged in plastic jars or tubes, as shown by Superslick Tuning Slide Grease, Giardinelli Brass Tuning Slide Grease and Fat Cat Tuning Slide Grease. Generally speaking, creams tend to be more work-intensive and messy than oils to apply, but many players consider them to be longer-lasting and smoother. Your own experimentation will tell you whether you agree, and it's worth trying out a few different types of tuning slide grease to discover what works best for you. Since it needs to be reapplied each time you clean your instrument, you'll have plenty of chances to test new ones!
Caring for your brass instrument isn't something that happens once: it's an ongoing task that lasts as long as you continue playing it. Keeping that instrument in good shape relies on having the supplies to do so, and tuning slide grease is certainly one of those supplies. Thankfully, with bottles, tubes and jars of grease small enough to pack alongside your instrument in its case, you'll never be missing that dab of lubrication when you need it.