Most (if not all) engineering jobs will require an engineering degree (unless you're in software/IT).
It depends on your degree. For science, honours is an extra year, where you conduct a research project and take honours-level courses. This is typically taken as a pathway towards a PhD.
For engineering, honours is typically incorporated as part of the degree for those who want to do it. In your final year, you're required to do some sort of project (alongside your normal courses). This project can either be conducted as a research thesis (honours), or a simpler project which can be done in a group. The honours thesis is typically more research-oriented, and requires more work. You are given the option of doing an honours project if your WAM is higher than 65. If you do an honours research project, then you graduate with honours as either first class if your WAM > 75, or second class if your WAM is between 65 and 75. You will not graduate with honours if your final WAM is below 65. Your honours research mark will make up about 25% of your final WAM. This is for USYD, but I'm fairly sure other universities also operate their engineering honours degrees in a similar manner.
Graduating with honours does make your degree look slightly nicer as it shows you have research experience, and typically brighter students will do an honours project. However, in terms of employment, I don't think it'd make a huge impact unless your research was related to what the company does (if not, then they won't really care). Keep in mind that some students also have absolutely garbage honours projects, but still end up graduating with honours, so having honours itself doesn't necessarily mean anything. I remember seeing one guy whose one honours presentation involved no original research at all. His topic was on solar sails, and his entire project was just talking about what they were and giving facts about them - kind of what you expect from a high school level research project, and in no way suitable as honours-level research. It looked like he just copied everything on wikipedia into his presentation the night before.
If you wish to do a PhD, then you should do honours. Typically, a student's PhD research will be somewhat related to their honours, which makes it easier to get into the program as the supervisors know who they are. However, it is not absolutely necessary. You can always jump from a straight bachelors (with no honours) to a PhD if you can prove yourself, though this is the exception rather than the norm.
For example, my engineering honours project was done with the School of Physics. After I graduated, I applied to both engineering and physics PhD programs (since I wasn't sure which one I wanted), and I got into both even though I didn't have a physics honours. This was because I had a good relationship with my physics supervisor, and my engineering honours research essentially substituted the physics honours (even though I never did the required coursework to obtain a physics honours). However, in most cases, getting into the science PhD programs typically require you to have honours in those relevant fields.
Most students have no idea what honours project they want to do until a few weeks before they need to choose, so it's something that you don't need to worry about for a very long time. Before you start your final year, the school will usually give out a list of all the projects being offered by professors within the faculty, and the students can speak to the professors if they're interested in a particular topic. You can always pick your own topic if you can find a professor willing to supervise you. You can also pick topics from other faculties like I did, as long as its remotely related (in the case of engineering, any quantitative research project) and the school signs off on it. Alternatively, if you're working part-time at an engineering firm and they want you to do some research for them, then you can choose to get them to supervise your research.