The battery trickle charger refers to a battery charger that charges at a low amperage.
Many battery chargers put out a variety of amperages, the idea being to charge a battery slowly or quickly depending on the need. Some are also designed to be left connected long-term without overcharging. So when you hear people talk about trickle chargers, that's typically what they're referring to.
For general use, any battery charger, or trickle charger, that puts out between about 1 and 3 amps will do, and you don't really need one with float mode monitoring unless you want to be able to leave it connected for some reason.
There are two main ratings for car battery chargers: amperage output and voltage. To charge a typical car battery, you need a 12V charger, but many car battery chargers have 6, 12, and even 24V modes.
In terms of amperage, car battery chargers typically put out anywhere between 1 and 50 amps for the charging mode. Some also have a jump start mode, where they can put out upwards of 200 amps, which is what it takes to turn over most starter motors.
The main thing that defines any charger as a trickle charger is that it either has a low amperage option, or it only puts out a low charging amperage. Most trickle chargers put out somewhere between 1 and about 3 amps, but there is no hard and fast rule on that.