Pros:
Very Tanky
Insane CC's
Good Engage/Disengage
Strong presence (Like roaming getting vision control).

Cons:
Vulnerable to poke
No Lane sustain
Risky play like if u misseed ur combo then you have no way out to defend urself or help teammates it can cause games throws

Leona is a notorious roam because of all of the CC that she has. If you can spare some time, ganking mid lane or top lane will often end up in a kill for your ally laner. Also try to gank in conjunction with your jungler; to increase the probability of getting a kill. There's good times and bad times to roam.

Good times are the following:

1) You're against a really passive lane. They don't want to fight, they won't let you engage - so just take your business elsewhere. Mid lane perhaps.

2) You've just recalled. Before heading bottom lane you have a chance to gank mid or top. They won't see it coming and, so long as your ADC doesn't die, it's a swell idea.

3) The enemy mid laner has no gap closers or has just burned their Flash/ult. This is a window wherein a chance to get a kill is much higher.

4) Dragon is up; and it's a good one! If you kill the enemy mid laner, you can much easily secure the Dragon with your jungler and ADC.

As for the bad:

1) Bot lane is pushed down to your tower. If you leave your ADC alone at this tower, there's a big chance that the enemy will decide to dive him. At the very least, the tower is in danger.

2) Your ADC has just arrived to lane after having recalled. This means he's lost out on some gold and XP and needs you to babysit him so he doesn't get zoned and lose out on more.

3) The enemy mid laner has 200 gap closers. If you roam, you will likely just waste your time.

Leona is strong at teamfighting with her crazy stats

If you're the initiator, keep in mind this: you shouldn't be one. Ideally, you want someone else to engage so that you are free to stick to your ADC and keep them safe. If you catch someone out; and that's why you're the initiator, then that's a different story. If you can get a good catch and onto a priority target, always go for it; especially late game.

Likewise you should not opt to be the primary tank for your team. You are very tanky with your W, but without it you will be less tanky than a solo laner tank could be. You simply don't have the right income. You won't be able to bulk up as hard as a tank top or tank jungler can.

Now being a peeler is exactly what you signed up for. Peeling is essentially keeping enemies off of your ADC. If you have a fed ADC, this is especially important. Stick close to your ADC and be ready to stun, root and stun again. Also stand in front of your ADC to intercept ultimates and projectiles.

https://youtu.be/x1W4bx-mWDY link for Leona combos