Password strength indicator does not, per se, guarantee stronger passwords - from a pure UX perspective the more complex your requirements are the more likely people are to click away, to use an existing password or to write it down hence making it harder for a human to remember but, all too often, only marginally more difficult for a computer to crack.
Most password strength indicators look at two things - length and mix of "characters". The most common I see is must be at least 8 characters long and contain at least one number or special character. However, these meters do nothing to prevent use of already known passwords as well as dictionary words.
For example, if I use pa55word as my password it meets all the requirements above yet it is has an entropy of 1 and an "instant" crack time. Even changing pa55word to p@55word makes no difference as it is such a common substitution - the problem here is the use of different forms of the word password which most strength checkers do not look at.
Mark Burnett did some great research in 2011 on 10,000 top passwords based on 6m publicly available cracked username and password combinations (https://xato.net/passwords/more-top-worst-passwords) and found "this list of the 10,000 most common passwords represents 99.8% of all user passwords." Admittedly, most of them are just letters or letters and numbers but, as seen above, substituting numbers or punctuation for letters alone is not enough.
There is a good example on xkcd of the flaws of most strength checkers - basically, if you ask someone which is stronger and harder to crack (a) Tr0ub4dor&3 OR (b) correcthorsebatterystaple then most would opt for (a) yet (b) is stronger with a 550 year crack time compared to 3 days for a though a is MUCH harder to remember for most users.
Based on this, Dropbox came up with a new password strength indicator based on entropy (http://en.wikipedia.org/wiki/Entropy) which is worth looking at especially then comparison they did of their library against many other commonly used systems on the web for three passwords and the findings were interesting with a broad difference in the strength rating of three passwords - qwER43@!, Tr0ub4dor&3 and correcthorsebatterystaple.
Ultimately, as this is about UX you need to be careful to find a balance between security and user friendliness. Do nothing and people will use password (used 32,000 times in the above research) yet make the rules too complex and people will write them down etc
We have opted not to use any sort of password strength indicator on our application but, instead, we simply prevent anyone using any words from the top 10,000 list - it isn't perfect by any chalk but then I am not sure anything is especially when passwords like qwER43@! are considered "weak" by zxcvbn so just how can you make users choose safe passwords without having to spend days educating them which is not something you can do when trying to get customers to sign up to web application and a message saying qwER43@! is a weak password is likely to annoy all but the most strong minded customer!